In transmitting data, or recording data onto a recording medium, e.g., magnetic disc, optical disc or magneto-optical disc, etc., modulation of data is carried out so as to become in conformity with transmission or recording. Block encoding is known as one of such modulation systems. This block encoding is adapted to block data train into units consisting of m.times.i bits (hereinafter referred to as data words) to convert such data words into code words consisting of n.times.i bits in accordance with the suitable code rule. In this case, when i is equal to 1, this code word is caused to be fixed length code, while when plural values can be selected as i, i.e., i is equal to 2 or more and conversion is made by i max=r which is the maximum i, that code word is caused to be variable length code. This block encoded code is generally represented as variable length code (d, k; m, n; r). In this expression, i is constraint length and r is the maximum constraint length. In addition, d and k respectively denote the minimum successive number of "0" and the maximum successive number of "0" falling (assigned) between successive "1" within the code series.
The modulation system used in the Compact Disc (CD) system as a more practical example will now be explained. In the compact disc system, EFM (Eight to Fourteen Modulation) system is used. Data words of 8 bits are subjected to pattern conversion into code words (channel bit data) of 14 bits thereafter to add respective margin bits of 3 bits for the purpose of reducing d.c. component (DSV) after undergone EFM to record, onto the disc, code words to which the margin bits are respectively added after undergone NRZI modulation. In this case, in order to satisfy the condition where the minimum successive number of logic "0" levels is 2 and the maximum successive number of logic "0" level is 10, conversion from 8 bits into 14 bits and addition of margin bits are carried out. Accordingly, the parameter of this modulation system is (2, 10; 8, 17; 1). When bit interval of the channel bit data train (recording waveform train) is assumed to be T, the minimum inverting (inversion) interval T.sub.min is 3(=2+1)T. Further, the maximum inverting interval T.sub.max is 11(=10+1)T. In addition, the detection window width T.sub.w is expressed as (m/n)xT, and its value is 0.47 (=8/17) T in the above-mentioned example.
Moreover, the minimum run length d' of the same symbols after undergone NRZI modulation is 3(=d+1=2+1), and the maximum run length k' of the same symbols is 11(=k+1=10+1).
In the above-described compact disc system, if pits on the optical disc are reduced in the linear velocity direction, the recording density can be caused to be high. In this case, the minimum pit length corresponding to the minimum inverting interval T.sub.min is reduced. When this minimum pit length is too smaller than the spot size of laser beam, detection of pits becomes difficult. This constitutes the cause of occurrence of error.
Further, in reproduction of the disc, when skew is applied to the reproduction surface of the disc, the error rate is deteriorated. The skew (angle) of the disc is gradient (inclined angle) that the disc and the optical axis form, and is classified into the skew (component) in the tangential direction which is the gradient that the pit train direction of the disc and the optical axis form, and the skew (component) in the radial direction which is the gradient that the direction perpendicular to the pit train of the disc and the optical axis form. With respect to the skew (component) in the tangential direction of these skew components, the error rate is deteriorated in a relatively short time. Such deterioration of the error rate results in decrease in the margin in designing the system.
Further, as the result of the fact that distribution of errors with respect to length of running (continuity) of the same symbols is examined with respect to respective directions of the skew, error with respect to the skew in the tangential direction mainly takes place in the case where the run length of the same symbols is short. In more practical sense, it has been found that since length of T.sub.min (d') is decoded into length of T.sub.min-1 (d'-1), the error rate is deteriorated. Namely, it has been found that, in the above-described EFM system, in the case where skew takes place in the tangential direction, when the bit interval of the recording waveform train is assumed to be T, error resulting from the fact that 3T which is the minimum inverting interval T.sub.min is decoded into 2T takes place to much degree.
Further, it has been found that such an error takes place to some degree also by perturbation such as the skew in the radial direction and/or defocus, i.e., shift (deviation) in the focal point, etc. Further, it has been found that in the case where perturbation such as skew or shift (deviation) in the focal point, etc. is enormously large, error resulting from the fact that 3T which is the minimum inverting interval T.sub.min is decoded into 1T also takes place.
On the other hand, in the optical disc, margin is allowed (tolerable) to some degree with respect to asymmetry of the disc in the production thereof. It is necessary that the case where reproduction waveform is asymmetrical in upper and lower directions with respect to the center level is also taken into consideration in reproduction.
Hitherto, as a method of correction by the signal processing with respect to deterioration of the error rate, there was the Viterbi decoding method. The Viterbi decoding method is one of the maximum likelihood decoding methods of allowing the code error to be small to search the shortest path of the geometrical distance, and is a method of ejecting the path of low possibility to thereby simplify search of probable value to carry out decoding. Further, in the Viterbi decoding method, algorithm for compensating the minimum inverting interval T.sub.min can be inclusively added.
However, the Viterbi decoding method has the drawbacks that the circuit therefor is complicated and the scale of the hardware becomes large. In addition, the Viterbi decoding method is required to remove the influence of asymmetry. In the system where asymmetry is allowed (tolerable) like the optical disc, optimization with respect to asymmetry becomes necessary. As a result, the circuit is further complicated.
As stated above, in the recording medium, e.g., optical disc, etc., there may take place the case where ensuring of the skew margin becomes difficult. Particularly, with respect to the tangential direction, there results less skew margin.
In addition, in the recording medium, e.g., optical disc caused to have high density, etc., since stable reproduction of the minimum inverting interval T.sub.min becomes difficult, the error rate is deteriorated.